ELIMINATING GIBB EFFECT FROM SEPARATION OF VARIABLES SOLUTIONS

To solve the Laplace equation on a rectangular domain with given nonho mogeneous Dirichlet boundary conditions, separation of variables is fr equently used. However the convergence of the resulting series solutio n will often be slow, due to the presence of Gibb's effects. A simple trick can avoid this and greatly increase the speed of convergence. Th is can illustrate to students how use of mathematical insight can give a practical benefit.